Relative detection efficiency of the World Wide LightningLocation Network

M. L. Hutchins,1 R. H. Holzworth,1 J. B. Brundell,2 and C. J. Rodger3

Received 18 May 2012; revised 18 October 2012; accepted 25 October 2012; published 13 December 2012.

[1] Using the detected energy per strokes of the World Wide Lightning Location Network(WWLLN) we calculate the relative detection efficiency for the network as if it had auniform detection efficiency. The model uses the energy statistics of located strokes todetermine which stations are sensitive to what stroke energies. We are then able to estimatethe number of strokes that may be missing from any given regions as compared to the best,most sensitive regions of the WWLLN network. Stroke density maps can be correctedwith the knowledge of how sensitive various regions of the network are operating.This new model for the relative WWLLN detection efficiency compensates for the unevenglobal coverage of the network sensors as well as variations in very low frequency (VLF)propagation. The model gives a way to represent the global distribution of strokes as ifobserved by a globally uniform network. The model results are analyzed in spatial andtemporal regimes, and the effects of a single VLF detector going offline are investigated inareas of sparse and dense detector coverage. The results are also used to show spatial,temporal and energy distributions as seen by the detection efficiency corrected WWLLN.

Citation: Hutchins, M. L., R. H. Holzworth, J. B. Brundell, and C. J. Rodger (2012), Relative detection efficiency of the WorldWide Lightning Location Network, Radio Sci., 47, RS6005, doi:10.1029/2012RS005049.

1. Introduction

[2] TheWorldWide Lightning Location Network (WWLLN)has been generating global lightning locations since 2004[Rodger et al., 2006, 2009a]. Since then the network hasgrown from 18 stations to over 60 as of August 2012.Additional stations have greatly improved the ability ofWWLLN to locate progressively weaker strokes [Rodgeret al., 2009a; Abarca et al., 2010]. However, the WWLLNnetwork does not observe lightning with the same detectionefficiency everywhere. This is due to variable WWLLN sta-tion coverage and the strong affect on very low frequency(VLF) radio propagation from orography and ionosphericconditions along the great circle path of a wave. This paperdemonstrates a technique which uses only data collected bythe WWLLN network itself, to estimate the relative detectionefficiency of each 5� � 5� pixel over the Earth compared tothe best average WWLLN detection efficiency. For instance,the lightning stroke density over central Africa, whereWWLLN station density is sparse, can now be compared tothe region of the Earth with the best detection efficiency, such

as North America. This paper does not provide an absolutedetection efficiency calculation.[3] WWLLN (see http://wwlln.net) determines the loca-

tion for nearly all lightning producing storms around theglobe in real time [Jacobson et al., 2006]. The network usesVLF radio wave receivers distributed around the globe toidentify the time of group arrival (TOGA) for the wavepackets from individual lightning-produced sferics [Dowdenet al., 2002]. A central processor combines the TOGAs todetermine the source locations over the spherical Earth. TheTOGA of the VLF wave packet developed by Dowden andBrundell [2000], is used rather than “trigger time” to pro-duce more uniform arrival times across the network. Strokelocations are determined using the TOGAs with a time ofarrival algorithm over the spherical Earth [see Rodger et al.,2009a, 2009b]. Knowledge of global stroke locations, withhigh temporal and spatial accuracy is beneficial for bothscientific and technical uses. WWLLN lightning locationdata have recently been used for advances in space science[Lay et al., 2007; Kumar et al., 2009; Collier et al., 2009;Holzworth et al., 2011; Jacobson et al., 2011], meteorology[Price et al., 2009; Thomas et al., 2010], detailed lightningphysics [Connaughton et al., 2010], and volcanic eruptionmonitoring [Doughton, 2010].[4] As of April 2012 WWLLN consisted of 60 VLF sta-

tions distributed around the world, with more stations con-tinuously being added to the network. The network improvesin accuracy and detection efficiency with increased stations;for example an increase in the number of WWLLN stationsfrom 11 in 2003 to 30 in 2007 led to a�165% increase in thenumber of lightning strokes located [Rodger et al., 2009a].As of 2011 the network located 61% of strokes to <5 km and

1Department of Earth and Space Sciences, University of Washington,Seattle, Washington, USA.

2UltraMSK.com, Dunedin, New Zealand.3Department of Physics, University of Otago, Dunedin, New Zealand.

Corresponding author: M. L. Hutchins, Department of Earth and SpaceSciences, University of Washington, Box 351310, Johnson Hall 070,Seattle, WA 98105, USA. (mlhutch@uw.edu)

©2012. American Geophysical Union. All Rights Reserved.0048-6604/12/2012RS005049

RADIO SCIENCE, VOL. 47, RS6005, doi:10.1029/2012RS005049, 2012

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54% to <15 ms with an estimated detection efficiency of about11% for cloud to ground flashes and >30% for higher peakcurrent flashes over the Continental United States [Hutchinset al., 2012b; Abarca et al., 2010; Rodger et al., 2009a].[5] A concern for all VLF networks is the nonuniform

propagation of VLF waves due to changing ionospheric andsurface conditions; this is true for networks monitoringlightning produced VLF signals like WWLLN, or thosemonitoring fixed-frequency communication transmitters likeAARDDVARK [Clilverd et al., 2009]. During the day thereis a larger ionospheric electron density at lower D-regionaltitudes. This causes the range of electron-neutral collisionfrequencies to overlap with the range of sferic wave fre-quencies, increasing the attenuation rate of the sferics. Thisincrease in electron number density is also seen in the changeof the reference ionospheric height, h′ [Wait and Spies,1960], during the day (h′ = 74 km) compared to during thenight (h′ = 87 km). There is a similar change in attenuationover the path of the sferic from the differences in the con-ductivity of the oceans (4 S/m), continents (10�2–10�4 S/m),and Antarctic/Arctic ice (10�5 S/m). The many path para-meters for a given sferic result in a highly variable attenuation[Volland, 1995].[6] Thus, independently determining the real-time detec-

tion efficiency has always been a challenging topic. Severalstudies have been conducted comparing the network to otherground based networks or satellite measurements [Lay et al.,

2004; Jacobson et al., 2006; Rodger et al., 2009a; Abarcaet al., 2010; Abreu et al., 2010]. These studies tend to belimited in either scope or in time due to the availability of datafrom other networks. Past work by Rodger et al. [2006]attempted to determine the global detection efficiency ofWWLLN using a theoretical model linked to observationsfrom a ground based commercial lightning network in NewZealand. In this paper a new method is developed for deter-mining the relative detection efficiency of WWLLN basedupon the recent network advancement of measuring theradiated energy of detected strokes [Hutchins et al., 2012a].[7] Developing a model of detection efficiency expands the

capabilities and uses for WWLLN. In particular a model thatdoes not rely on external comparisons to other networks orsensors is critical for obtaining a dynamic global view of net-work performance. Such a view will enable the network to beused with more confidence in areas of lower coverage andenable the network to be utilized with uniform detection effi-ciency in work requiring lightning rates and densities. Thisuniform performance will allow for more accurate studies ofglobal phenomena such as the short time (<10 minute) vari-ability of the global electric circuit, comparative lightningclimatology between regions, and production rate estimationsof transient luminous events and terrestrial gamma ray flashes.The detection efficiency model can combine with the mea-surements of stroke energy and regional absolute detectionefficiency studies to advance research in global effects oflightning such as estimating the total sferic energy transferredto the magnetosphere in the form of whistler waves.

1.1. Calculating the Radiated Stroke Energy

[8] Every WWLLN sferic packet includes the TOGA anda measure of the root mean square (RMS) electric field ofthe triggered waveform. The RMS electric field is takenin the 6–18 kHz band over the triggering window of 1.33 ms.The U.S. Navy Long Wave Propagation Capability (LWPC)code described by Ferguson [1998] is utilized to model theVLF propagation from each located stroke to determine thenecessary stroke energy to produce the measured RMSelectric field (in the VLF band) at each WWLLN station.Using the measured RMS field at each station, the radiatedenergy of each detected stroke is found. In 2010 WWLLNobserved a global median stroke energy of 629 J, with a 25%average uncertainty in the measured energy. The global andregional distribution of energy is shown in Figure 1a. Of allthe detected strokes 97% have corresponding energy values.[Hutchins et al., 2012a].[9] In Figure 1a the statistical error bars (Poisson statis-

tics) are not plotted as they would be on the order, or smallerthan, the line width. It is important to note that the distri-bution of strokes in each region is lognormal [Hutchinset al., 2012a] with the main differences in the total strokesdetected and the median energy, which is 399 J, 1101 J, and798 J for the Americas (�180�E to �60�E), Africa (�60�Eto 60�E), and Asia (60� E to 180�E) respectively. An overalllower detection efficiency over Africa, particularly for lowenergy strokes, causes median energy to be higher than theother regions. Along with each region the energy distribu-tion is lognormal from an hourly timescale to the annualdistribution. In Figure 1b the annual lognormal distributionis shown with a monthly, daily, and hourly distribution. It is

Figure 1. (a) WWLLN stroke energy distribution for theglobe (black), the Americas (blue), Asia (green) and Aftica/Europe (red). (b) WWLLN global stroke energy distributionfor a year (2010), month (June 2010), day (15 June 2010),and hour (09 UTC 15 June 2010). Grey lines are statisticalcount errors.

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not until the hourly distribution that the errors are noticeable,and the distribution is still fairly lognormal.

2. Minimum Detectable Energy

[10] The first step in calculating the relative detectionefficiency for the entire network is working out the minimumstroke energy thatWWLLN can detect at a given location andtime. This process starts by finding the detection threshold ateach station, converting it to an energy value at each locationin the world, and then selecting the minimum detectablenetwork energy at every location based on the minimumobservable energy from each station. Detailed examples ofhow this works are given next for single stations and for thenetwork as a whole.

2.1. Station Threshold

[11] At each WWLLN station the threshold for triggering onan event (and calculating the TOGA at that station) is dynam-ically selected depending on observed activity at that station asdescribed in Section 5.3 ofRodger et al. [2006]. Presently everyWWLLN station automatically adjusts the triggering thresholdto send an average of 3 packets per second to the central pro-cessor. For instance, when a station is detecting many strokes,the trigger threshold at that station is raised to maintain a steadyflow of sferic packets. Since a station can only measure theelectric (or magnetic) field of an event it cannot accuratelydiscern whether a sferic comes from a nearby weak stroke or astrong distant stroke; for the case of the strongest lightningstrokes the discharge could be on the other side of the Earthfrom the WWLLN station and still be detected.[12] The effect of the variable trigger threshold can be

seen in Figure 2a which is a 2 - D histogram of number ofstrokes with specific RMS field and UT values on 15 June2010 for the Dunedin, New Zealand, WWLLN station(�45.864�N, 170.514�E). In Figure 2b the threshold can beseen as the lower cutoff of the triggered RMS field strengthdistribution, the station threshold is reconstructed hourly asthe 5th percentile value (red line) of the distribution. The thresh-old value varies relatively slowly over the course of the day.

2.2. Station Minimum Detectable Energy

[13] The minimum detectable energy (MDE) is the mini-mum energy a lightning stroke must radiate in the VLF to be

detected by WWLLN or a WWLLN station (denoted net-work MDE and station MDE respectively). The MDE is afunction of space, time and station threshold. Each stationhas a variable threshold which varies slowly during the day.Slow ionospheric variations can also affect the MDE bychanging the VLF attenuation and detected RMS field.[14] Every hour the reconstructed minimum RMS field

necessary to trigger an event is calculated and converted to astroke energy. To make this conversion the same method ascalculating the radiated energy per stroke is used asdescribed in Hutchins et al. [2012a]. This results in a stationMDE for every point on a 5� � 5� global grid, which is thestroke energy necessary at that location to trigger a TOGAcalculation at the given station. As an example the map ofthe MDE for our Dunedin station (data shown in Figure 2) isshown in Figure 3. Figure 3 applies only to strokes detectedat this one station in Dunedin, a similar map can be gener-ated for every WWLLN station. The high MDEs in Figure 3over the Antarctic, Western Africa, and Greenland are due tothe high VLF attenuation over ice, and imply that Dunedin isvery unlikely to detect strokes with energy less than theMDE if they were to occur in these regions.

Figure 2. (a) The evolution of the triggered RMS field strength distribution (in arbitrary units) for theDunedin WWLLN station with the red line showing the 5th percentile value. (b) The 9 UTC slice ofthe distribution, with the 5th percentile value marked (red line).

Figure 3. The minimum detectable energy (MDE) for theDunedin station at 9 UTC on 15 June 2010. The regions ofhigh MDE are due to poor VLF propagation over ice fromthose regions to Dunedin station. The white line shows theterminator.

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[15] In order to locate a stroke, WWLLN requires TOGAvalues from at least five stations in order to conduct ade-quate fit error analysis. For every 5� � 5� grid cell all of theminimum stroke energies from currently active WWLLNstations are ordered. An example for one cell is shown inTable 1. The 5th lowest from this list is used as the networkMDE, because at least five stations can trigger on thatenergy value. In other words, WWLLN cannot detect astroke until it has a radiated energy which is above thetrigger threshold at five or more WWLLN stations. A map ofthe network MDE is shown in Figure 4. Similar to the stationMDE map for our Dunedin station, Figure 3, there are higherMDE values above the Arctic and Antarctic ice regions.[16] Regions of the network with higher MDE, from either

increased VLF attenuation, station thresholds or sparsecoverage, preferentially detect a higher ratio of energeticstrokes to all strokes. For example southern Africa has ahigher MDE than other regions and the median energy,shown in Figure 1a is correspondingly higher. Converselyregions with low MDE, such as the Americas, show a lowermedian energy.

3. Relative Detection Efficiency

[17] The next important step in calculating the relativedetection efficiency is to establish the relationship betweenthe network MDE and relative detection efficiency. Therelative detection efficiency is a measure of how well a givenlocation in the network is being observed relative to the best

region in the network. In a given grid cell the network MDEis compared to the total WWLLN energy distribution of thepast seven days. For a given network MDE value the frac-tion of total strokes above the network MDE gives the rel-ative detection efficiency. The past seven day distribution isused as the base distribution in order to average over diurnaland station performance variations. This lognormal basedistribution is assumed to be representative of a single uni-versal distribution of stroke energies that could be detectedglobally by a uniform WWLLN.[18] For example, if a location has an network MDE of

100 J, then the number of strokes in the past seven daysabove 100 J (grey area, Figure 5a) is compared to the totalnumber of strokes which were located in that location inthose seven days. In this case the grey area has a count of2.6 � 106 strokes and the total number of WWLLN strokesis 2.9 � 106 strokes, so for this network MDE of 100 J therelative detection efficiency is 90%. Similarly if a locationhas a high network MDE value there will be few strokeswith energy above it, so it will have a low relative detectionefficiency.[19] This calculation is done for a range of hypothetical

network MDE values which produces a curve shown inFigure 5b, to give the relationship between MDE and rela-tive detection efficiency. This relationship is establishedonce per day, and it is used to produce hourly maps of rel-ative detection efficiency for that day. This is done by takingthe hourly maps of network MDE and applying this relationto every 5� � 5� point on the globe for every hour to convertthe network MDE to the relative detection efficiency.

Table 1. Ordered List of Station MDE Values at�25�N, 20�E and09 UTC on 15 June 2010a

Station Name MDE (J)

Davis, Antarctica 34.5Ascension Island 169.2SANAE Base, Antarctica 193.9Perth, Australia 2268.3Rothera, Antarctica 2413.5Tel Aviv, Israel 4701.1… …Honolulu, Hawaii 1.35 � 108

Dunedin, New Zealand 5.09 � 108

aThe fifth lowest value (in bold) is the network MDE at this location.

Figure 4. The minimum detectable energy (MDE) for theentire WWLLN network at 9 UTC on 15 June 2010.

Figure 5. (a) The seven day energy distribution with thestrokes above the MDE of 100 J shown in grey. (b) The frac-tion of strokes above 100 J to total strokes gives a relativedetection efficiency of 0.9, shown as a circle. The fractionfor all possibleMDE values is shown as the curve in Figure 5b.

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[20] The relative detection values given by this process areonly in reference to the energy distribution of the past sevendays as seen by WWLLN. If a region has a relative detectionefficiency of 100% then the region is able to detect all of thedetected stroke energies present in the 7-day network energydistribution. The corrections from the relative detectionefficiency maps can be used to generate lightning densitydistributions as though WWLLN had global uniform cover-age at the same level as that of the best parts of the network.This is because the method does not correct the network toabsolute stroke counts, just to a globally uniform performingWWLLN.

3.1. Hourly Maps

[21] A set of four hourly maps from 15 June 2010 showingthe networks relative detection efficiency every 6 hours from00 UTC to 18 UTC is presented in Figure 6. Stations that wereoperational for the hour shown are displayed in white and sta-tions that were not operational are black (operational taken totriggering >500 strokes/hour). The four major competingeffects on the detection efficiency are the day/night terminator,local stroke activity, station density, and station performance.The day/night terminator effect can be seen as it moves from00 UTC (Figure 6a) through 18 UTC (Figure 6d). An increasein local stroke activity in North American afternoon (Figure 6a)causes a decrease in detection efficiency as nearby stations raisetheir triggering thresholds. Station density is coupled with sta-tion performance, since when a station is not operating opti-mally it has a similar effect as removing that station, the effectof station performance is discussed in a later section.[22] Figure 7 shows the daily relative detection efficiency

from the average of the hourly maps, here grey stations were

only operational part of the day. This average map is morerepresentative of the relative detection efficiency for the dayand it shows behavior that is expected based on the distri-bution of stations: lower detection efficiency over most ofAfrica with higher detection efficiency over and around thePacific and North America. The low detection efficiencyover Antarctica, parts of Siberia, and Greenland are due tothe high attenuation of VLF propagating subionosphericallyover ice. Conversely the high detection efficiency overNorth America, Western Europe, and Oceania, are due to the

Figure 6. Relative detection efficiency maps for 00, 06, 12, and 18 UTC on 15 June 2010. Stations areshown as triangles with operational stations in white and nonoperational in black. The minimum value ofdetection efficiency is set at 5% to prevent unphysical corrections.

Figure 7. Daily average relative detection efficiency for 15June 2010. Stations are shown as triangles with operationalstations in white, nonoperational in black, and operationalfor part of the day in grey. The minimum value of detectionefficiency is set at 5% to prevent unphysical corrections.

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high station density and low attenuation of VLF over ocean.In order to prevent unphysical overcorrections, a minimumrelative detection efficiency of 5% has been set for all of therelative detection efficiency maps.

4. Analysis

4.1. Distribution Changes

[23] As shown in the previous sections the relative detec-tion efficiency values in a given day are derived from theWWLLN observed stroke energy distribution from the pre-vious seven days, this allows for direct comparisons within aday and for nearby days, but it does not take into account thechanging distribution from changes in the network. As morestations are added to the network additional low-energystrokes will be detected and the overall energy distributionwill shift toward lower values. When the overall networkdistribution changes between years, then for a given regionthe relative detection efficiency can change even if thatregion of the network has detected the same distribution ofstrokes.[24] One way to examine the change in the distribution of

energy is to examine the temporal variability of the medianof the global WWLLN energy distribution, the median of theseven day distribution is shown in Figure 8. The medianenergy varies from the three year median by 52% with thedaily median value ranging from 400 J to 2000 J. The vari-ability is caused by ionospheric changes not accounted for inthe ionospheric model used. Several jumps in the medianenergy (e.g., Dec 2009 and Dec 2010) are caused by changesin the primary calibrated WWLLN station [see Hutchins

et al., 2012a] such as gain changes. The slow increase toAug 2011 was due to a change of the primary calibratedstation from the Dunedin, New Zealand station to the ScottBase, Antarctica station. It is important to note that since thedetection efficiency is relative to the past seven days, therelatively slow changes in median energy do not stronglyaffect the detection efficiency and highlight how the relativedetection efficiency cannot correct for absolute overall net-work performance.

4.2. Temporal Variability

[25] The evolution of the network can be seen as anincrease in the global average relative detection efficiency,calculated by averaging all grid cells of the each hourlymaps for a day. While no region can have a relative detectionefficiency over 100%, as regions improve with more stationsthey will approach 100% and increase the global averagedetection efficiency. The global average relative detectionefficiency from April 2009 through October 2011 is shownas the green line in Figure 9. In the figure the total number ofoperational stations is shown as the black line, and it has astrong correlation to the global averaged detection efficiencywith a correlation value of 0.86. With more stations strate-gically added to the network the 7-dayenergy distributionwill also change to include more low energy strokes andincrease the average relative detection efficiency.[26] While Figure 9 shows an overall increase in the

number of network stations and hence detection efficiency,Figure 10 shows similar curves for just low-latitude regions(�30�N to 30�N, blue), a single location near Florida(�85�E, 30�N, red), and a single location near South Africa(25�E, �20�N, green). Removing high latitude regionsincreases the overall detection efficiency but does notchange the overall upward trend shown by the blue curve inFigure 10. When the region near Florida is examined it canbe seen that it remains fairly close to 1.0 for the entire dataset, with downward trends during local summer months dueto increased local lightning activity. The region near SouthAfrica has a steady increase in detection efficiency exceptduring a large drop out which occurred in the middle of2011, caused by one of the African stations going offline.This shows the global detection efficiency tracks the

Figure 8. Median stroke energy of the 7-day distributionobserved by WWLLN. The relative detection efficiency ofthe network is based on this 7-day energy distribution.

Figure 9. The number of WWLLN stations operating(black) and the global average relative detection efficiency(green) for April 2009 through October 2011.

Figure 10. Daily variation of average detection efficiencyfor the globe (black), low-latitudes (�30�N to 30�N, blue),over Florida (�85�E, 30�N, red), and over South Africa(�25�E, �20�N, green).

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network as a whole, but it cannot be used as an accurateproxy for smaller spatial scales.[27] The local time variability over the region near Florida

is shown in black in Figure 11 and shows a total variabilityof about 4.9%. The largest drop in the relative detectionefficiency occurs in the afternoon, near the peak in locallightning activity at 3 pm. This drop is due to the nearbystations raising their detection threshold in response todetecting more local strokes. For this location the effects oflocal activity dominates over the expected day/night effectdue to changes in VLF propagation.[28] The variability for the region near South Africa is

shown as the dotted line in Figure 11, there is a total vari-ability of 25.5%. There is an overall decrease in relative thedetection efficiency during the day when the sferics arepropagating over the continent. The best in relative detectionefficiency occurs in the middle of the night when the stationsin Africa have less nearby activity and sferics are able topropagate more readily under a night ionosphere. Comparedto the Florida region there is a much higher dependence onday and night conditions as well as a much wider range ofvariability.

4.3. Station Outage Effects

[29] While the overall performance of the network trendsalong with the total number of stations, the effects a singlestation turning on or off can have an effect on a large regionof the global but only small effect on the network as a whole.To test the influence of single stations a day of data wasrandomly selected, 16 June 2010, and the entire data werereprocessed with just the Honolulu, Hawaii station (�158�E,21�N) removed from the raw data and again with just theMaitri, Antarctica station (12�E, �71�N) removed. Themaps of the daily average with and without these stations areshown in Figure 12. For Hawaii the change is fairly local toits region in the Northeast Pacific Ocean, but leads to littleeffect across the entire network. In the case of Maitri there isa larger effect since it is located in a region of sparse detectorcoverage and covers much of the southern Atlantic.[30] The daily average global relative detection efficiency

dropped from 64% to 63% without Hawaii and from 64% to

53% without Maitri. The detection efficiency in the grid cellover Hawaii dropped from 85% to 78% and from 45% to7.4% in the grid cell over Maitri. A plot of the total changebetween the daily averages in Figure 12 is shown inFigure 13.

5. Results

[31] The detection efficiency model can be applied toglobal maps of stroke density to estimate, or correct for theglobal stroke density which would be seen if WWLLN had auniform spatial and temporal coverage. This does not correctfor the overall absolute detection efficiency (11% for CGflashes in the United States [see Abarca et al., 2010], rather

Figure 11. Average local time variation of detection effi-ciency over Florida (�85�E, 30�N, solid) and South Africa(�25�E, �20�N, dashed), from 2009–2011.

Figure 12. Relative detection efficiency map of 16 June2010 for (a) the complete network, (b) the network withthe Hawaii station (black star, �158�E, 21�N) removed,and (c) the network with Maitri station (black star, 12�E,�71�N) removed. Stations are shown as triangles with oper-ational stations in white, nonoperational in black, and oper-ational for part of the day in grey.

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it corrects for the areas with less WWLLN coverage. Thehourly stroke density plots are corrected by dividing thecounts in each grid cell by the relative detection efficiency ofthat cell. For example a grid cell with 100 strokes and anefficiency of 80% would be corrected to 125 strokes. Thestroke density from 2011, Figure 14, had the model correc-tions applied hourly with the condition that a 5� � 5� gridcell needed at least two strokes to have a correction applied.A second condition was that a minimum relative detectionefficiency of 5% was set for the model.[32] The total number of strokes for 2010 was 1.4 � 108

(4.4 strokes/second), and after applying the model the totalwas 2.0 � 108 strokes (6.3 strokes/second). In 2011 the totalnumber of strokes was 1.5 � 108 (4.8 strokes/second) with amodel-corrected value of 1.9 � 108 (6.0 strokes/second). In2010 63% of the global area between �60� latitude had arelative detection efficiency of at least 80% and in 2011 thisarea increased from 66% to 72%. If we assume that theglobal lightning flash rate was a constant 46 flashes/secondas determined by satellite measurements using the OpticalTransient Detector and Lightning Imaging Sensor [Cecilet al., 2011; Christian et al., 2003] for both years, thiswould imply a corrected global absolute detection efficiencyfor cloud to ground and in-cloud flashes of 13.7% for 2010and 13.0% in 2011.

[33] The corrected yearly density is shown in Figure 15,aside from the overall increase in number counts theimportant feature is the relative count rates over the US,Africa, and Southeast Asia. In the uncorrected Figure 14 thepeak stroke density in Asia and America are similar whileAfrica is about �1–10% of these values (also shown inFigure 1a). In the corrected maps we can see that the peakdensity in Africa is much closer in magnitude to that seenfor America and Asia, and the relative densities match thedistributions seen by OTD [see Christian et al., 2003,Figure 4]. The total increase in stroke counts is shown inFigure 16 with the greatest increases occurring over land, inparticular central Africa.

6. Conclusion

[34] A relative detection efficiency model is developed forWWLLN based on the WWLLN observed stroke energydistribution. The model is examined on various temporalscales as well as performance changes due to station outageeffects. The model is applied to the 2011 WWLLN data setto produce a corrected map of stroke activity, matching theexpected characteristics of satellite data. Work on comparing

Figure 13. The difference in detection efficiency for 16 June 2010 with (a) Hawaii and (b) Maitri stationscompletely removed from processing.

Figure 14. The raw 2011 global stroke density measuredby WWLLN.

Figure 15. The 2011 global stroke density measured byWWLLN and corrected for the relative detection efficiencyof the network. Note the large change in the African conti-nent relative to Figure 14.

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distant regions is now possible as the network data can becorrected to a uniform global level of performance. Futurework will focus on achieving a model for absolute detectionefficiency.

[35] Acknowledgments. The authors wish to thank the World WideLightning Location Network (http://wwlln.net), a collaboration among over50 universities and institutions, for providing the lightning location dataused in this paper.

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Figure 16. The increase in stroke density due to the rela-tive detection efficiency corrections for 2011. Uncorrectedand corrected stroke densities shown in Figures 14 and 15,respectively. The increase is plotted on the same scale asthe previous two figures.

HUTCHINS ET AL.: RELATIVE DETECTION EFFICIENCY OF WWLLN RS6005RS6005

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